The data suggests that both parties had an incentive to tend towards deescalating the conflict over the years. What exactly that incentive was remains unclear, but the trend towards a decrease in the number of troops for the British and a decrease in the number of fatalities caused by the IRA stands on its own. However, given the nature of the relationship in the data, we must conclude within the confines of this paper that H1 is false without further evidence. Of the eight years that the British stationed more troops in the North, six were followed by an increase in the number of fatalities in the next year. Of course, the IRA increased fatalities in ten years during this period, indicating that they were not only responding to the number of troops that the British were sending overseas to maintain control of the region. Because the IRA adopted a strong, zero tolerance position against allowing British troops to maintain a presence in Northern Ireland, it seems that decreases in troop numbers did not affect their yearly strategy in any appreciable way. Instead, they focused on the presence of British troops per se and geared their campaign towards complete removal of these forces. The relationship shown cannot be said to be anything more than coincidence, and there is not enough data to draw any statistically significant conclusions about the relationship between the number of troops stationed in Northern Ireland and the fluctuations in the number of fatalities caused by the IRA.
We have found that a graphical relationship existed between these two variables during this period of time, one that we have not shown to be statistically significant but is nevertheless worthy of comment. The next step in analyzing this conflict would be to determine why this relationship manifested in the way that it did. Gathering more
nuanced, fine-tuned data would be the first step in helping to further this analysis. A statistical analysis controlling for outside variables would help us better understand how the Provisionals decided to wage their campaign and what factors on the British side of the equation they were most responsive to. The Troubles were a complicated time for both parties. While these particular games have been constructed to display the conflict between the British government and the Provisional IRA, there were many more actors and groups involved, including other Irish republican groups, loyalist Irish groups that aided the British in combat, and even foreign governments at some points. Perhaps some other party influenced the course of events beyond what is manifestly visible in the data. Future research should examine what other factors may have caused this relationship to manifest itself. Additionally, a more detailed analysis will be required to determine whether the relationship between the variables is causal or merely a correlation.
However, my second hypothesis shows more promise under scrutiny. H2 predicted that the statements of IRA leaders would show a commitment to the continuation of their campaign based on the presence of British troops in Northern Ireland. And indeed, a level of blame shifting seems to be present in their justifications of violence. This all-or-nothing way of viewing the conflict, coupled with blame-shifting processes, appears to be much more helpful in explaining why the IRA escalated their campaign at certain points during its course than the simple fluctuation of troop numbers. The evidence for this hypothesis seems to indicate that the IRA’s commitment to its ideology was stronger than strategic concerns like stemming the flow of troops into the North. That is not to say that they ignored such considerations, but the statements of the Provisional leadership indicate that ideology was a more important motivating factor than
pragmatic concerns. Of course, it is possible that the leaders of the IRA simply touted their ideological dedication to signal a commitment to violence, when they were really responding to strategic concerns. Private communiqués between top-level IRA officials would prove helpful in deducing what really drove the IRA to alter the overall tone of its campaign.
Appendix: More on Game Theoretic Models
I will construct a bare 2x2 game so that the qualities of the game can be further explained. In this game there will be two players, each with two courses of action open to them, and each course of action will be assigned a numerical utility ranging from 1 to 4, with 4 being the outcome most desirous to the player and 1 being the outcome that is least desirous. The simplest way to depict this game is with a square subdivided into four squares:
Conventionally, the side on the left depicts player 1’s options, and the side on top represents player 2’s options. Each subdivided half of the sides represents a choice available to the game’s players:
So in this simplified model, players have two options available to them. The next step is to assign utility values to all of the possible outcomes (AA, AB, BA, and BB) based on their desirability to each player. By convention, the first value in the square is the utility assigned to that outcome by player 1, and the second value is the utility assigned by player 2. For simplicity’s sake, we will assign utility values between 1 and 4, first for player 1:
And then for player 2:
This particular formulation of a 2x2 game is what is known as a prisoner’s dilemma, as we will demonstrate later. But first we will discuss the most basic elements of this game. The most preferable outcome for each actor is to play option B while the opponent plays
option A, as indicated by the utility value 4. The second most preferable outcome is for both players to play option A. The third most preferable is for both players to play option B. Finally, the least preferable strategy is to play option A while the opponent plays option B.
Additionally, each player will prefer option B no matter what the opponent chooses. Note that if player 2 chooses option A, then player 1 benefits more from playing option B, because their payoff will be 4 rather than 3. Similarly, if player 2 chooses option B, then player 1 would also be expected to play option B, because their payoff will be 2 as opposed to 1. This indicates that the game is symmetric, meaning that the same strategy preference holds true for player 2 when responding to player 1’s
choices.81 Because B is preferable regardless of what the other player is expected to choose, we call B a dominant strategy. When the two dominant strategies of the players overlap, we have what is called a Nash equilibrium (which is the 2,2 payoff in the lower right square).82 A Nash equilibrium occurs when neither player has an incentive to change their strategy from a position without a credible guarantee from the other party, because they will be worsening their utility payoff. The dilemma is made clear when we consider that both players would be better off if they were to play strategy A, since their payoffs would both be 3 rather than 2. But because B is always preferable to A, the equilibrium will hold despite the existence of a better outcome for both parties. This state of the game is called Pareto-inefficient, because there exists an outcome that is more beneficial to both parties, but that cannot realistically be reached without extensive trust between both parties, thus demonstrating the Prisoner’s Dilemma.
81 Pavel, “Basics of Game Theory,” 17. 82 Ibid., 23.
The next model we will outline is the game tree. There are two ways to approach the construction of a game tree from the outset, and we must determine which is more useful in explaining the phenomenon we are choosing to model. Because this paper will analyze violence as a response to certain government spending decisions, it makes more sense to develop a two player game tree. However, first we will construct a simple game tree showing possible interplay between two players. An easy way to model this is to use the game of rock paper scissors. It might be noted that rock paper scissors is a game that is played simultaneously, but modeling it forces the interplay to be divided into steps. Yet the implications remain the same. Each player must make a decision based on the expected behavior of an opponent, and these choices taken together produce distinct outcomes. Oftentimes interactions in the international arena occur simultaneously, or at least without knowledge of what choice the other player will pursue. In this way, interactions are similar in both models. Of course, the decisions being modeled in terms of terrorism are responses rather than predictions, but the logic holds just the same.
In order to model a game of rock paper scissors, we need a starting point. The first relevant decision is the one made by player 1 regarding whether they will throw rock, paper, or scissors. Thus:
Player 1 faces a simple choice. We will assume for simplicity’s sake that they will consider choosing each move with a 1/3 probability. Therefore, if this were the entire
game, player 1 would choose one of rock, paper, or scissors 100% of the time. However, there is a response from player 2 that must also be considered. Because player 2 has the exact same three moves available to them their segment of the tree will simply be a duplicate of player 1’s tree branching off of each of player 1’s choices, like so:
Above is a completed game tree of one round of rock paper scissors. On the right we see nine terminal nodes, each representing a final state of the game (player 1 playing rock and player 2 playing rock, player 1 playing rock and player 2 playing paper, and so on). Because player 1 will play rock, paper, or scissors with probability 1/3, if we assign the same stipulation to player 2 we reach the conclusion that each terminal node will occur with probability 1/9, because each outcome occurs with probability 1/3 * 1/3.